A Variational Upper-Bound Method for Plane Strain Problems

[+] Author and Article Information
Wei-Ching Yeh, Yeon-Sheng Yang

Department of Mechanical Engineering, National Central University, Chung-Li, Taiwan, 32054 R.O.C.

J. Manuf. Sci. Eng 118(3), 301-309 (Aug 01, 1996) (9 pages) doi:10.1115/1.2831029 History: Received September 01, 1993; Revised April 01, 1995; Online January 17, 2008


In this paper, a variational upper-bound (VUB) method is proposed. It is the method that determines an upper-bound solution using variational calculus. By using the method, a set of so called “naturally boundary conditions,” which were all ignored in past investigations, can be theoretically derived for the rigid/plastic interface assumed to be arbitrary function in prior. This method is shown to be applicable to the cup ironing problem. From the result we can clearly indicate the role of these natural boundary conditions which reasonably account for the effect of friction on the pattern of metal flow. The VUB method not only presents an improvement on the traditional upper-bound method, but also favorably agrees with experimental result of Nielsen et al. (1963) in calculating upper-bound energy.

Copyright © 1996 by The American Society of Mechanical Engineers
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